Research interests

I am interested in resolution-based and tableaux-based decision
procedures for decidable fragments of first-order logic, including
fragments resulting from the relational, semi-functional and
optimised functional translation of decidable propositional
modal logics.
See, for example,
De Nivelle, Hustadt, and Schmidt
(2000),
Hustadt and Schmidt
(2000a,
1999a).

Reasoning in non-classical logics

I'm concerned with the design and analysis, both theoretical
and empirical, of modal and temporal theorem provers.
Some details of our findings
are presented here. Related publications concerning modal theorem provers are,
for example, Hustadt and Schmidt
(2000b,
1999c,
1998a).
Concerning temporal logic, I have been involved with the
development of TRP, TRP++, and their evaluations. See,
for example,
Hirsch and Hustadt (2001a);
Hustadt and Konev (2003);
Hustadt, Konev, Riazanov and Voronkov (2004);
Hustadt, Konev and Schmidt (2005;
Hustadt and Schmidt (2002b);
Konev, Degtyarev, Dixon, Fisher and Hustadt
(2005).

Agent Logics

I've also investigated proof methods for temporal logics of
knowledge and belief, and more recently general frameworks for
the combination of temporal and modal logics, in particular,
the KARO framework.
For further details see, for example,
Hustadt, Dixon, Schmidt and Fisher
(2000);
Hustadt, Dixon, Schmidt, Fisher, Meyer, van der Hoek
(2005,
2001a,
2001b).

Web Ontologies

Together with Boris Motik and Ulrike Sattler, University of
Manchester, I been involved in the development of a decision
procedure the web ontology languages SHIQ and SHIQ(D) based
on the basic superposition calculus. This approach offers a
radical alternative to tableaux calculi for such languages.
See
Hustadt, Motik and Sattler (2005a,
2005b,
2004a,
2004b,
2004c);
Motik, Sattler and Hustadt (2003a).

MSPASS - an enhancement of the first-order theorem prover SPASS
with a translator of modal formulae and formulae of the relational calculus into
first-order logic with equality.

MKE - an implementation of a tableaux-based decision procedure for basic modal
logic.

pdl-tableau -
an implementation of the tableau calculus introduced in
De Giacomo and Massacci (2000), "Combining Deduction and Model Checking into Tableaux and Algorithms for
Converse-PDL" (Information and Computation 162, pp. 117-137).

TABSPASS - a modified version of the first-order theorem prover SPASS which
simulates derivations of tableaux-based decision procedures for basic modal logic.

TRP -
a protoypical implementation of a theorem prover for propositional linear-time logic
based on the temporal resolution calculus.

TRP++ -
a C++ implementation of a theorem prover for propositional linear-time logic
based on the temporal resolution calculus, developed by
Boris Konev.

TeMP -
a C++ implementation of a theorem prover for the monodic fragment of first-order
linear-time temporal logic over expanding domains based on the temporal resolution
calculus, developed by Boris Konev.
Uses the Vampire
theorem prover as theorem proving kernel.

TSPASS.
a C implementation of a fair theorem prover for the monodic fragment of first-order
linear-time temporal logic over expanding domains based on the temporal resolution
calculus, developed by Michel Ludwig.
Uses the SPASS theorem prover as `computational engine'.